It has already been proven that deep equilibrium models with a single layer are equivalent to models with a finite number of layers and the converse as well. That you can get the performance of a DEQ using a finite number of layers.

The fixed point nature of DEQs means that they inherently have a concept of self assessment how close they are to the solution. If they are at the solution, they will simply stop changing it. If not, they will keep performing calculations.